an investment of $9,875 earns 4.8% interest compounded monthly over 12 years. approximately how much…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P=$9875$, $r = 0.048$ (since $4.8%=0.048$), $n = 12$ (compounded monthly), and $t = 12$ years.

Step2: Calculate the value of $(1+\frac{r}{n})^{nt}$

First, calculate $\frac{r}{n}=\frac{0.048}{12}=0.004$. Then, $nt=12\times12 = 144$. So, $(1 + 0.004)^{144}$. Using a calculator, $(1.004)^{144}\approx1.718$.

Step3: Calculate the final amount $A$

$A=P(1+\frac{r}{n})^{nt}=9875\times1.718\approx17065$.

Step4: Calculate the interest earned

The interest earned $I=A - P$. So, $I\approx17065 - 9875=7190$. The closest answer to this value is $$7458$.

Answer:

B. $$7,458$